Answer:
(3, 7 ) and (2, 2 )
Step-by-step explanation:
Given the 2 equations
y = x² - 2 → (1)
8 = 5x - y → (2)
Rearrange (2) expressing y in terms of x
y = 5x - 8 → (3)
Substitute y = x² - 2 into (3)
x² - 2 = 5x - 8 ← subtract 5x - 8 from both sides
x² - 5x + 6 = 0 ← in standard form
(x - 3)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 2 = 0 ⇒ x = 2
Substitute these values into (3) for corresponding values of y
x = 3 : y = 5(3) - 8 = 15 - 8 = 7 ⇒ (3, 7 )
x = 2 : y = 5(2) - 8 = 10 - 8 = 2 ⇒ (2, 2 )
